Question

A triangle has sides with lengths of 3, 7, and 2. What is the radius of the triangles inscribed circle?

Answer 1

This is not a triangle.

Explanation:

Use the triangle inequality theorem to see that these side lengths cannot form a valid triangle.

The theorem states that for any triangle with sides `a,b,c`, the following three inequalities hold:

`a+b>c`

`b+c>a`

`c+a>b`

Here, we see that `3+2>7` is untrue, so the sides do not describe a triangle.